Fabrice Chauvet

Optimization of cyclic production systems: a heuristic approach

In this paper, the expression production systems refers to flow shops, job shops, assembly systems, Kanban systems, and, in general, to any discrete event system which transforms raw material and/or components into products and/or components. Such a system is said to be cyclic if it provides the same sequence of products indefinitely. A schedule of a cyclic production system is defined as soon as the starting time of each operation on the related resource is known. It has been shown that, whatever the feasible schedule applied to the cyclic production system, it is always possible to fully utilize the bottleneck resource. In other words, it is always possible to maximize the throughput of such a system. As a consequence, we aim at finding the schedule which permits to maximize the throughput with a work in process as small as possible. We propose a heuristic approach based on Petri nets to find a near-optimal, if not optimal, solution. We also give a sufficient condition for a solution to be optimal.

Simple bounds and greedy algorithms for decomposing a flow into a minimal set of paths

Given arbitrary source and target nodes s, t and an s–t-flow defined by its flow-values on each arc of a network, we consider the problem of finding a decomposition of this flow with a minimal number of s–t-paths. This problem is issued from the engineering of telecommunications networks for which the task of implementing a routing solution consists in integrating a set of end-to-end paths. We show that this problem is NP-hard in the strong sense and give some properties of an optimal solution. We then propose upper and lower bounds for the number of paths in an optimal solution. Finally we develop two heuristics based on the properties of a special set of solutions called saturating solutions.

Managing a Pool of Self Service Cars

Abstract This paper addresses the public transportation problem using electric cars. The system under consideration is a self-service system. The management of this new form of transportation means includes two issues: the redistribution of the cars among the stations and the recharge problem. In this paper, we describe how to manage these two issues.